Technical University of Catalonia

“Seismic Design and Retrofit of Buildings and Bridges” 2016

Capacity curve of a steel frame (Exercise No. 10)
Conduct a pushover analysis of the steel frame described in Figure 1; as a result, provide the capacity curve,
i.e. horizontal displacement of beam vs. base shear. After this curve, determine the actual over strength
factor (represented by 0 in American regulations and by u / 1 in EC-8).

Figure 1. Steel frame

The structure consists of two columns being 3 m high and a beam being 8 m long. Columns are hinged in
their bases and beam-column connections are rigid. Columns / beam are made with HEB 200 / IPE 330
profiles. Gravity loads are represented by a uniformly distributed law on the beam (25 kN/m). Steel grade
is S275 (fy = 275 MPa).

Flexure plastic hinges are the only source of nonlinearity; if the hinges are near the member ends, it can be
assumed that they are formed exactly al joints. The moment-rotation law (M-) is shown in Figure 2.

Figure 2. Moment-rotation law of plastic hinges

. y = Wpl fy l / 6 E I for beam and
y = (Wpl fy l / 6 E I) (1 – N / A fy) for columns.9 of
EC-3 (EN-1993 2005).2. but must be considered in columns. the use of Excel. Only hand calculations
are permitted. Therefore. A. 6. N is the demanding axial force in columns
(compression is positive) at the onset of the first plastic hinge.
 To familiarize with American and European regulations. Technical University of Catalonia
“Seismic Design and Retrofit of Buildings and Bridges” 2016
My and y are the yield moment and the rotation angle. certainly. I Wpl
are area. Influence of axial force in yield moment of
beams can be neglected.
the use of any structural analysis software (either global or local) is prevented.
The objectives of this exercise are:
 To perform all the operations manually. l is member length. respectively. E is steel modulus of elasticity. moment of inertia and plastic modulus respectively. to understand deeply the basis of pushover analysis. MatLab or similar software is possible. follow formulation described in art.